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%I #9 Jan 10 2019 10:23:46
%S 4,7,9,12,14,19,21,26,30,35,39,46,50,57,63,70,76,85,91,100,108,117,
%T 125,136,144,155,165,176,186,199,209,222,234,247,259,274,286,301,315,
%U 330,344,361,375,392,408,425,441,460,476,495,513,532,550,571,589,610,630,651,671
%N Number of 3 X n binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.
%H R. H. Hardin, <a href="/A266936/b266936.txt">Table of n, a(n) for n = 1..158</a>
%F Empirical: a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6).
%F Empirical g.f.: x*(4 + 3*x - 2*x^2 - 4*x^3 - 3*x^4 + 4*x^5) / ((1 - x)^3*(1 + x)*(1 + x + x^2)). - _Colin Barker_, Jan 10 2019
%e Some solutions for n=4:
%e ..0..0..0..1....0..0..1..1....1..1..1..1....0..0..1..1....0..0..1..1
%e ..1..1..1..0....1..1..0..1....1..1..1..1....1..1..0..0....1..1..0..0
%e ..1..1..1..0....1..1..1..0....1..1..1..1....1..1..0..0....1..1..1..1
%Y Row 3 of A266935.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 06 2016
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